Image Completion Using a Diffusion Driven Mean Curvature Flowin A Sub-Riemannian Space
نویسندگان
چکیده
In this paper we present an implementation of a perceptual completion model performed in the three dimensional space of position and orientation of level lines of an image. We show that the space is equipped with a natural subriemannian metric. This model allows to perform disocclusion representing both the occluding and occluded objects simultaneously in the space. The completion is accomplished by computing minimal surfaces with respect to the non Euclidean metric of the space. The minimality is achieved via diffusion driven mean curvature flow. Results are presented in a number of cognitive relevant cases.
منابع مشابه
Spacelike hypersurfaces in Riemannian or Lorentzian space forms satisfying L_k(x)=Ax+b
We study connected orientable spacelike hypersurfaces $x:M^{n}rightarrowM_q^{n+1}(c)$, isometrically immersed into the Riemannian or Lorentzian space form of curvature $c=-1,0,1$, and index $q=0,1$, satisfying the condition $~L_kx=Ax+b$,~ where $L_k$ is the $textit{linearized operator}$ of the $(k+1)$-th mean curvature $H_{k+1}$ of the hypersurface for a fixed integer $0leq k
متن کاملRICCI CURVATURE OF SUBMANIFOLDS OF A SASAKIAN SPACE FORM
Involving the Ricci curvature and the squared mean curvature, we obtain basic inequalities for different kind of submaniforlds of a Sasakian space form tangent to the structure vector field of the ambient manifold. Contrary to already known results, we find a different necessary and sufficient condition for the equality for Ricci curvature of C-totally real submanifolds of a Sasakian space form...
متن کاملACTION OF SEMISIMPLE ISOMERY GROUPS ON SOME RIEMANNIAN MANIFOLDS OF NONPOSITIVE CURVATURE
A manifold with a smooth action of a Lie group G is called G-manifold. In this paper we consider a complete Riemannian manifold M with the action of a closed and connected Lie subgroup G of the isometries. The dimension of the orbit space is called the cohomogeneity of the action. Manifolds having actions of cohomogeneity zero are called homogeneous. A classic theorem about Riemannian manifolds...
متن کاملSubjective Surfaces and Riemannian Mean Curvature Flow of Graphs
A geometric model for segmentation of images with missing boundaries is presented. Some classical problems of boundary completion in cognitive images, like the pop up of subjective contours in the famous triangle of Kanizsa, are faced from a surface evolution point of view. The method is based on the mean curvature evolution of a graph with respect to the Riemannian metric induced by the image....
متن کاملSpacelike hypersurfaces with constant $S$ or $K$ in de Sitter space or anti-de Sitter space
Let $M^n$ be an $n(ngeq 3)$-dimensional complete connected and oriented spacelike hypersurface in a de Sitter space or an anti-de Sitter space, $S$ and $K$ be the squared norm of the second fundamental form and Gauss-Kronecker curvature of $M^n$. If $S$ or $K$ is constant, nonzero and $M^n$ has two distinct principal curvatures one of which is simple, we obtain some charact...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008